Austin-Healey Motors Inc.is currently levered.It used to be all-equity,but it recently borrowed and used the money to repurchase 50,000 shares.Financial details for the current and old capital structures are presented in the table below.
Assume that Austin-Healey generates perpetual annual EBIT at a constant level.Assume that all cash flows occur at the end of the year and we are currently at the beginning of a year.Assume that taxes are zero.Assume that all of net income is paid out as a dividend.Assume that the debt is perpetual with annual coupons at 3%.Assume that individual investors can borrow and lend at the same interest rate (and with the same terms)as corporations.
Nigel Mansell is a shareholder in Austin-Healey who owns 5,000 shares.After the repurchase,Nigel is unhappy with his dividends.How many shares does Nigel have to buy (sell)in order to return his annual cash flows to what they were under the all-equity capital structure? (Assume that Nigel had the same number of shares under the old structure.)

Question

Quizplus · Accepted Answer

Under the all equity capital structure the investor will receive annual cash flows of 5,000 × $1.50 = $7,500. To achieve this cash flow under the levered capital structure he will have to sell some shares and invest the proceeds in a bond (lend the money). Denote the number of shares owned originally as O. Denote the number owned after this trade as N. Denote the stock price at which the shares are sold as P. The interest earned on shares sold is: Interest earned = (O - N) × P × k_d If we add the interest earned to the dividends received after the trade, then we can solve for N. The annual cash flows from the investment are: Cash Flows = N × DPS + Interest Earned The first term is the value of dividends received at his new ownership level of N under the levered capital structure. We set this expression equal to $7,500 (the annual cash flows desired by the investor) and we solve for N. $7,500 = N × DPS + Interest $7,500 = N× DPS + ((O - N) × P × k_d $7,500 = N × DPS + ((O × P × k_d) - (N × P × k_d)) N x DPS - (N × P × k_d) = $7,500 - (O × P × k_d) N x (DPS - P × k_d) = $7,500 - (O × P × k_d) N = 11ea7fdb_fc5e_5f9b_a768_43e4aeb5f3c9_TB2902_11 N = 11ea7fdb_fc5e_5f9c_a768_ab70db77a37d_TB2902_11 = 2,500 Since N < O, this means that Mansell sells 2,500 shares.